AI Dictionary › Fondamenti AI
PCA (Analisi delle componenti principali)
Principal Component Analysis, or PCA, is a dimensionality reduction technique that transforms a set of possibly correlated numeric variables into a smaller number of new variables, called principal components, which summarize most of the original information using as few dimensions as possible. It is one of the most widely used tools for simplifying complex datasets without losing what truly matters.
The technique identifies the directions along which the data varies the most: the first principal component is the direction of maximum variability in the data, the second is the direction of maximum remaining variability, perpendicular to the first, and so on. Mathematically this is achieved by computing the eigenvectors and eigenvalues of the covariance matrix of the original variables, standardized beforehand to prevent those with larger scale from dominating the result. By ranking components by how much variability they explain, it is possible to keep only the first few and discard the rest, drastically reducing the number of variables with a contained and quantifiable loss of information.
It is used to compress high-dimensional datasets before training other models, to visualize complex data in two or three dimensions understandable to the human eye, to eliminate redundancy between strongly correlated variables, and as a preprocessing step in fields like genomics, image processing and financial portfolio analysis. It also reduces the risk of overfitting in subsequent models by simplifying the feature space they must work with.
The mathematical foundations of PCA trace back to a 1901 paper by the British mathematician and biostatistician Karl Pearson, who introduced it as a method for finding the lines and planes that best approximate a set of points in space. The technique was later reformulated and made practically applicable in statistics by the American statistician Harold Hotelling in 1933, who is also credited with the name principal components, and it has remained one of the most solid and widely used tools of multivariate analysis ever since.
From our network
Magellano GPS: Fleet Tracking Made Simple
Real-time GPS tracking, remote engine lock, fuel and CO₂ reporting for your fleet.
Visit magellanogps.com →From the Agora Intelligence blog
📱 Download the Android app (beta) iOS coming soon
Say what you mean. Get what you need.
Grace Certified, the AI coach that trains and certifies your prompt engineering, by Agora Intelligence.